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evablogger [386]
3 years ago
6

What is the perimeter of △ABC?

Mathematics
1 answer:
timofeeve [1]3 years ago
7 0
<h3>Given</h3>
  • ΔABC
  • A(-3, -1), B(0, 3), C(1, 2)
<h3>Find</h3>
  • the length of the perimeter of ΔABC to the nearest tenth
<h3>Solution</h3>

The perimeter of a triangle is the sum of the lengths of its sides. The length of each side can be found using the Pythagorean theorem. Effectively, each pair of points is treated as the end-points of the hypotenuse of a right triangle with legs parallel to the x- and y-axes. The leg lengths are the differences betweeen the x- and y- coordinates of the points.

The difference of the x-coordinates of segment AB are 0-(-3) = 3. The y-coordinate difference is 3-(-1) = 4. So, the leg lengths of the right triangle whose hypotenuse is segment AB are 3 and 4. The Pythagorean theorem tells us

... AB² = 3² +4² = 9 +16 = 25

... AB = √25 = 5

You may recognize this as the 3-4-5 triangle often introduced as one of the first ones you play with when you learn the Pythagorean theorem.

LIkewise, segment AC has coordinate differences of ...

... C - A = (1, 2) -(-3, -1) = (4, 3)

These are the same leg lengths (in the other order) as for segment AB, so its length is also 5.

Segment BC has coordinate differences ...

... C - B = (1, 2) -(0, 3) = (1, -1)

The length of the line segment is figured as the root of the sum of squares, even though one of the coordinate differences is negative. The leg lengths of the right triangle used for finding the length of BC are the absolute value of these differences, or 1 and 1. Then the length BC is

... BC = √(1² +1²) = √2 ≈ 1.4

So the perimeter of the triangle ABC is

... AB + BC + AC = 5 + 1.4 + 5 = 11.4 . . . . perimeter of ∆ABC in units

_____

Please be aware that the advice to "round each step" is <em>bad advice,</em> in general. For real-world math problems, you only round the final result. You always carry at least enough precision in the numbers to ensure that there will not be any error in the final rounding.

In this problem, the only number that is not an integer is √2, so it doesn't really matter.

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Claire is 2 year younger than her sister. The
natta225 [31]

Given:

Claire is 2 year younger than her sister.

The  sum of ages is no less than 44 years.

To find:

Inequality and find the youngest age Claire can  be.

Solution:

Let the age of Claire be x.

Her sister's age = x+2

Sum of their ages is no less than 44 years. It means the sum ages is greater than or equal to 44.

x+(x+2)\geq 44

2x+2\geq 44

2x\geq 44-2

2x\geq 42

Divide both sides by 2.

x\geq 21

It means, Claire age can be greater than or equal to 21. So, the youngest age Claire can  be 21 years old.

Therefore, the required inequality is  2x+2\geq 44 and the correct option is B.

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3 years ago
Read 2 more answers
If 5x – 4 = 31, what is the value of x?​
Lunna [17]

Answer:

x = 5 \frac{2}{5}

Step-by-step explanation:

Hi there!

So, to answer this problem, I'll use the reverse method.

31 - 4 = 27,

So how many times, can 5 go into 27?

The closest factor of 5 to 27 is 25.

5 can go in to 27,  5 times.

Continuing on, there is a 2 left over, so the answer to your question is

x = 5 \frac{2}{5}

5 · 5 \frac{2}{5} - 4 = 31

Let me know if I am incorrect and I will attempt to find the right answer for you.

<em>waffletowne</em>

7 0
2 years ago
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Math math math math math <br> i need help<br> tysm :) &lt;3
stiv31 [10]

Answer:

C. x^14

Step-by-step explanation:

(x^9)^0 is 1

(x^7)^2 is x^14

x^14*1 is x^14

The Answer is C. x^14

Hope this helps!

5 0
2 years ago
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